Hello, I want to develope a 3-d code which will be a flow solver with turbulence and spray models and based on the transformed equations ( solver for a body fitted grid ). Since in finite volume method, there are a huge number of schemes, I am feeling confused because each has its own advantages & disadvantages. Out of all algorithms, I have decide that I will use either K.C.Karki's (1988, karki & patankar, NHT publication ) scheme, based on staggered grid or S.Mujumdar's scheme, which is based on non staggered scheme of Rhie and Chow ! Though the non staggered scheme approach looks simpler, I am not feeling confident whether it will really be stable or will it give problems regarding convergence ( specifically as I have to solve spray also). Kindly guide me for this ! Thanking you !

The non-staggered grid approach is used by all major FV-based commercial CFD codes and it proves to be fine. I would be interested to know why you think it will cause problem with sprays since codes like STAR-CD (from Computational Dynamics), VECTIS (from Ricardo) and FIRE (from AVL) all used successfully for internal engine combustions.

Dear Jon Thanks for your reply. But after the literature survey I found that first non staggered scheme was proposed by Rhie and Chow, then it was critised by S. Majumdar and he proposed his own scheme. The scheme of S. Majumdar was later critised by Date, and he put his own scheme.Later Date critised his own scheme and put another scheme. Due to all this I am not feeling confident about choosing some.

Given your apparent starting point I would strongly suggest obtaining a working code and adapting it. KIVA seems an obvious choice given your interest in sprays but there are several others.

Non-staggered schemes are usually significantly simpler to code. In general, convergence/stability is not a major concern. A much bigger problem is poor accuracy in the presence of significant non-linear pressure gradients. If your application has significant swirl then it might be a good idea to look at other schemes or, at least, move away from the large amount of pressure smoothing introduced by a "straight" Rhie & Chow scheme.

I would also advise not going into print stating that Rhie & Chow introduced the first non-staggered scheme. For example, many compressible methods and many finite element methods were non-staggered in the 20 odd years prior to Rhie&Chow. The paper seems to have had a large impact because around that time most groups with working incompressible staggered codes were looking to move to general body-fitted coordinates and having problems with the practicalities of using covariant or contravariant base vectors.